5.3.2 Klein bottle

If x lies on an edge, then each of the two points in [x] has a half-disc-like neighbourhood (see Figure 107). When we identify edges, these neighbourhoods fit together to form disc-like neighbourhoods in the Klein bottle.

Figure 107

If x is a vertex, then each of the four points in [x] has a half-disc-like neighbourhood (as the shape of a quarter-disc – see Figure 108). When we identify edges, these neighbourhoods fit together to form a disc-like neighbourhood in the Klein bottle.

Figure 108